Accelerated Jarzynski estimator with deterministic virtual trajectories
Accelerated Jarzynski estimator with deterministic virtual trajectories
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具有确定性虚拟轨迹的加速 Jarzynski 估计器
DOI：
10.1103/physreve.105.054120
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发表时间：
2022
影响因子：
2.4
通讯作者：
Hasegawa Yoshihiko
中科院分区：
文献类型：
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作者：
Ishida Nobumasa;Hasegawa Yoshihiko
Jarzynski估计器是一种强大的工具，它利用非平衡统计物理在数值上获得概率分布的配分函数。该估计器通过Jarzynski方程重构了具有模拟朗之万动力学轨迹的配分函数。然而，原始估计量由于依赖于随机动力学的稀有轨迹而收敛缓慢。本文提出了在哈密顿动力学下引入增广状态空间中生成的确定性虚拟轨迹来显著加速收敛的方法。我们从理论上证明，与具有朗之万动力学和谐波势零方差估计的朴素估计器相比，我们的方法实现了二阶加速度。本文还对三种多模态分布进行了数值实验，并给出了一个实际例子，表明所提出的方法优于传统方法，并给出了理论解释。
The Jarzynski estimator is a powerful tool that uses nonequilibrium statistical physics to numerically obtain partition functions of probability distributions. The estimator reconstructs partition functions with trajectories of the simulated Langevin dynamics through the Jarzynski equality. However, the original estimator suffers from slow convergence because it depends on rare trajectories of stochastic dynamics. In this paper, we present a method to significantly accelerate the convergence by introducing deterministic virtual trajectories generated in augmented state space under the Hamiltonian dynamics. We theoretically show that our approach achieves second-order acceleration compared to a naive estimator with the Langevin dynamics and zero variance estimation on harmonic potentials. We also present numerical experiments on three multimodal distributions and a practical example in which the proposed method outperforms the conventional method, and we provide theoretical explanations.